Let's take a bunch of lines, like in (A) (We could have bezier curves, either. Let's say: open paths)
Let's take then a circle (or another closed path), like (B)
Let's put the each above/below the other(s) like (C)
Is there in Inkscape a (quick) way to get (D) or (E) NOT just as the result of a CLIPPING MASK, but as a set of inscribed(D)/outscribed(E) paths?
I mean: paths beginning/ending where the circle happened to "trim" the rest.
Starting from a bunch of lines, you can combine them with Ctrl+K (refer to Path menu):
Then you have to put the second path in the desired position:
Now, you can cut the path with Ctrl+Alt+/:
Here come the boring part: each line is cutted in two or more segments. You have to select them one by one (I have colored the stroke while selecting, just to see the selected paths):
You can move the selection and the work is done:
Note that the selection is made by single paths, you can combine or group them to simplify further operations.